# R/score.irt.r In psych: Procedures for Psychological, Psychometric, and Personality Research

#### Documented in scoreIrt.1plscoreIrt.2pltest.irt

```#revised August 31, 2012 to allow for estimation of all 0s or all 1s
#modified March 10, 2016 to allow for quasi Bayesian estimates using normal theory
#which doesn't seem to do what I want to do, so we are not doing it
#June 30-July 7 , 2016  Trying to make it faster by parallelizing the code and
#reducing the number of items to score when using keys.
#uses local minima -- problematic for small number of items
#corrected various problems with finding total (sum) scores  7/4/16
#starting to make parallel for speed
#seems to result in at least a factor of 2 improvement
#when using stats from fa, the discrim parameter are not necessarily in the order from a keyslist
#this is only a problem if selecting items from a larger set of items
#fixed this August 21, 2016
#the irt.2 function (dichotomous items) iis much slower than the polytomous solution
#probably because we took parallelization one step too far
#I have not removed that extra level

####  The scoring of dichotomous data
#the function to do 2  parameter dichotomous IRT\

#these should be put into the score.irt.2 function for speed
#taken out for debugging purposes
irt.2par.norm <-  function(x,delta,beta,scores) {
fit <- -1*(log(scores*(1-pnorm(beta*(delta-x))) + (1-scores)*(1-pnorm(beta*(x-delta)))))
mean(fit,na.rm=TRUE)
}
#This does the logistic fit
irt.2par <- function(x,delta,beta,scores) {
fit <- -1*(log(scores/(1+exp(beta*(delta-x))) + (1-scores)/(1+exp(beta*(x-delta))) ))
mean(fit,na.rm=TRUE)
}

#These next two functions were added to add limits to the fitting functions for the cases of all wrong and all right
irtLimit.2par <- function(x,delta,beta,scores) {
minItem <- which.min(delta*beta)
maxItem <- which.max(delta*beta)
fit <- -scores*log(1/(1+exp(beta*(delta-x)))) - (1-scores)*log(1/(1+exp(beta*(x-delta)))) - log(1/(1+exp(beta[minItem] *(delta[minItem]-x-1)))) - log(1/(1+exp(beta[maxItem] *(x-delta[maxItem]-1 )))   )
mean(fit,na.rm=TRUE)
}

irtLimit.2par.norm <-  function(x,delta,beta,scores) {
minItem <- which.min(delta*beta)
maxItem <- which.max(delta*beta)
fit <- -( scores*log(1-pnorm(beta*(delta-x)))   +(1-scores)*log(1-pnorm(beta*(x-delta)))   +log(1-pnorm(beta[minItem]*(delta[minItem]-x -1 ))) + log( 1-pnorm(beta[maxItem]*(x- delta[maxItem] -1 )) )          )
mean(fit,na.rm=TRUE)
}

"score.irt.2" <-
function(stats,items,keys=NULL,cut=.3,bounds=c(-4,4),mod="logistic") {
#find the person parameters in a 2 parameter model we use deltas and betas from irt.discrim and irt.person.rasch
#find the person  parameter
#This does the normal fit
#has several internal functions

##the next two are the parallelized functions
#parallelize by subject seems most helpful?ms
bySubject <- function(i,count.f,total.f,items.f,discrim.f,diffi.f) {

#First we consider the case of all right or all wrong
#but we also need to consider the person with no data!
if (count.f[i] > 0) {
beta=discrim.f[!is.na(items.f[i,])]
delta=diffi.f[!is.na(items.f[i,])]

if((sum(items.f[i,],na.rm=TRUE) ==0 )  || (prod(items.f[i,],na.rm=TRUE) ==  1 )) {

if(sum(items.f[i,],na.rm=TRUE) ==0 ) {
#the case of all wrong
# we model this as
#although probably we don't need to do this anymore
if(mod =="logistic") {
myfit <-  optimize(irtLimit.2par,bounds,beta=beta,delta=delta,scores = rep(0,sum(!is.na(items.f[i,] )))) } else {

myfit <-  optimize(irtLimit.2par.norm,bounds,beta=beta,delta=delta, scores = rep(0,sum(!is.na(items.f[i,]))))

}
theta <- myfit\$minimum
fit <- myfit\$objective
}  else {
if(prod(items.f[i,],na.rm=TRUE) ==  1 ) {

if (mod=="logistic") {  myfit <- optimize(irtLimit.2par,bounds,beta=beta,delta=delta,scores = rep(1,sum(!is.na(items.f[i,])))) #do the logistic fit
} else {
myfit <- optimize(irtLimit.2par.norm,bounds,beta=beta,delta=delta,scores = rep(1,sum(!is.na(items.f[i,]))))
} #do a normal fit function
theta <- myfit\$minimum
fit <- myfit\$objective
}
}} else {

scores=t(items.f[i,!is.na(items.f[i,])]) #make this numeric in the case of weird (highly missing) data
if(mod=="logistic") {
myfit <- optimize(irtLimit.2par,bounds,beta=beta,delta=delta,scores=scores)  #do the logistic fit
} else {
myfit <- optimize(irtLimit.2par.norm,bounds,beta=beta,delta=delta,scores=scores)} #do a normal fit function
theta <- myfit\$minimum
fit <- myfit\$objective  #fit of optimizing program

}} else  {#cat("\nno items for subject",i)
total.f[i]  <- NA
theta <- NA
fit  <- NA

}  #end if count ... else
return(list(theta,total.f[i],fit) )
}  #end bySubject

#parallelize by factor
#this is the the one to use when parallelized
bigFunction <- function(f,n.obs,stats,items,keys=NULL,cut=.3,bounds=c(-5,5),mod="logistic") {
nf <- length(stats\$difficulty)
diff <- stats\$difficulty[[f]]
cat <- dim(diff)[2]

if(nf < 2) {#discrim <- drop(stats\$discrimination)
discrim <- stats\$discrimination  # although I need to check this with keys
if(!is.null(keys)) {discrim <- discrim * abs(keys)}
} else {discrim <- stats\$discrimination[,f]
if(!is.null(keys)) {discrim <- discrim * abs(keys[,f])
}}

###

fit <- rep(NA,n.obs)
theta <- rep(NA,n.obs)

if(is.null(keys)) {#drop the items with discrim < cut

items.f <- items[,(abs(discrim[,f]) > cut) ,drop=FALSE]  #get rid of the those items that are not being processed for this factor
diffi.f <- diff[(abs(discrim[,f]) > cut)]   #and the redundant diffi
discrim.f <- discrim[(abs(discrim[,f]) > cut),drop=FALSE ]  #and get rid of the unnecessary discrim values

} else { #the  case of scoring with a keys vector

items.f <- items[,(abs(keys[,f]) > 0) ,drop=FALSE]  #get rid of the those items that are not being processed for this factor
discrim.f <- discrim[(abs(keys[,f]) > 0),drop=FALSE ]  #and get rid of the unnecessary discrim values
diffi.f <- diff[(abs(keys[,f]) > 0)]   #and the redundant diffi
}

diffi.vect <- as.vector(t(diffi.f))

#discrim.F.vect <- rep(discrim.f,each=cat)
#discrim.f <- discrim[(abs(discrim > cut)),drop=FALSE]
discrim.F.vect <- as.vector(t(discrim.f))

if(is.matrix(discrim)) discrim.F.vect <- drop(discrim.F.vect)
total <- rowMeans(t(t(items.f)*sign(discrim.F.vect)),na.rm=TRUE)
count <- rowSums(!is.na(items.f))
#We can speed this up somewhat if we don't try to fit items with 0 discrim (i.e., items that do not load on the factor or are not keyed)

#do it for all subject for this factor
#now, lets parallelize this for each subject as well
#this is probably a bad idea, for it leads to an amazing amount of overhead in terms of memory and processes
#mapply for debugging,  mcmapply for parallel
#lets just try mapply to see if it gets around the problem
#actually, making this mcmapply and the call to bigFunction mapply seems to be the solution
#especially when we are doing scoreIrt.1pl or scoreIrt.2pl which is already doing the parallelsim there

subjecttheta <-mcmapply(bySubject,c(1:n.obs),MoreArgs = list(count,total,items.f,discrim.f,diffi.f))  #returns a list of theta and fit

subjecttheta <- matrix(unlist(subjecttheta),ncol=3,byrow=TRUE)
theta <- subjecttheta[,1]
total <- subjecttheta[,2]
fit <- subjecttheta[,3]
theta [theta < bounds[1]] <- bounds[1]
theta[theta > bounds[2]] <- bounds[2]
#  if((!is.null(keys)) & (all(keys[,f] == -1) || (sign(cor(discrim,keys[,f],use="pairwise")) < 0) )) {theta <- -theta
#if((!is.null(keys)) & (all(keys[,f] == -1)  )) {theta <- -theta
#                             total <- -total}

nf <- length(stats\$difficulty)
n.obs <- dim(items)[1]
nvar <- dim(items)[2]
# scores <- matrix(NaN,nrow=n.obs,ncol=nf*3)

#scores <- list(nf*3)

scores <- list(theta,total,fit)
return(scores)
} # end of bigFunction

#now do the scoring one factor at a time but allowing multiple cores

#we now start score.irt.2 proper
#this finds scores using multiple cores if they are available

nf <- length(stats\$difficulty)
n.obs <- dim(items)[1]

min.item <- min(items,na.rm=TRUE)  #uses local minima --probably  problematic for small number of items
items <- items - min.item #this converts scores to positive values from 0  up  (needed to do the fitting function)

#this parallels by factor  which in turn is parallelized by subject in bySubject
#use mapply for debugging, mcmapply for parallel processing
#since we are already parallelizing by scale when we call scoreIrt.1pl or .2pl, this is not necessary to parallelize
scores <- mcmapply(bigFunction,c(1:nf),MoreArgs=list(n.obs=n.obs,items=items,stats=stats,keys=keys, cut=cut, bounds=bounds, mod=mod))

nf <- length(stats\$difficulty)
scores <- matrix(unlist(scores),ncol=nf*3)
scores <- scores[,c(seq(1,nf*3,3),seq(2,nf*3+1,3),seq(3,nf*3 +2,3))]
colnames(scores) <- paste(rep(c("theta","total","fit"),each=nf),1:nf,sep="")
return(scores)

}#end of score.irt.2
###################

#####################

"score.irt.poly" <-
function(stats,items,keys=NULL,cut=.3,bounds=c(-4,4),mod="logistic") {
#find the person parameters in a 2 parameter model we use deltas and betas from irt.discrim and irt.person.rasch
#find the person  parameter
#created July 4, 2011
#revised Dec 31, 2016 to match irt.2
# this optimizes the logistic function,
#   irt.2par.poly <- function(x,delta,beta,scores) {
#    fit <- -(scores*log(1/(1+exp(beta*(delta-x)))) + (1-scores)*log(1/(1+exp(beta*(x-delta)))))
#    mean(fit,na.rm=TRUE)
#    }
#
#  irt.2par.poly.norm <-  function(x,delta,beta,scores) {
#   fit <- -1*(log(scores*(1-pnorm(beta*(delta-x))) + (1-scores)*(1-pnorm(beta*(x-delta)))))
#   mean(fit,na.rm=TRUE)
#   }

####The function that is  parallelized
big.poly <- function(f,n.obs,stats,items,keys=NULL,cut=.3,bounds=c(-5,5),mod="logistic") {
nf <- ncol(stats\$discrimination)
#for (f in 1:nf) { #do it for every factor/scale
diff <- stats\$difficulty[[f]]

if(nf < 2) {discrim <- stats\$discrimination
if(!is.null(keys)) {discrim <- discrim * abs(keys)
} } else {discrim <- stats\$discrimination[,f]
if(!is.null(keys)) {discrim <- discrim * abs(keys[,f])
}
}
cat <- dim(diff)[2]
total <- rep(NA,n.obs)
fit <- rep(NA,n.obs)
theta <- rep(NA,n.obs)
item.f <- t(items)
item.f[abs(discrim) < cut] <- NA  #this does not change the item, just the temp version of the item
item.f <- t(item.f)

###
if(!is.null(keys)) {item.f <- item.f[,(abs(keys[,f] )> 0) ,drop=FALSE]  #get rid of the those items that are not being processed for this factor
discrim.f <- discrim[(abs(keys[,f]) > 0),drop=FALSE ]  #and get rid of the unnecessary discrim values
diffi.f <- diff[(abs(keys[,f]) > 0),byrows=TRUE]   #and the redundant diffi

diffi.vect <- as.vector(t(diff[(abs(keys[,f]) > 0),byrows=TRUE]))
discrim.F.vect <- rep(discrim.f,each=cat)
} else { discrim.f <- discrim
diffi.f <- diff
diffi.vect <- as.vector(t(diff) )
discrim.F.vect <- rep(discrim.f,each=cat)
}

## notice that this is vectorized and does it for all subjects
#seem to have solved the problem of missing items which are reversed.

total <- rowMeans(t(t(item.f )* as.vector(sign(discrim.f))),na.rm=TRUE) #fixed 11/11/11 to be as.vector

# total.positive <- rowMeans(t(t(item.f)* as.vector(sign(discrim.f) > 0)),na.rm=TRUE)
# total.negative <- rowMeans(t(t(item.f)* as.vector(sign(discrim.f) < 0)),na.rm=TRUE)
##

num.keyed <- rowSums(!is.na(item.f))
num.reversed <- rowSums(!is.na(item.f[,discrim.f < 0,drop=FALSE]))

total <- total + num.reversed * (max.item- min.item+1)/num.keyed  + min.item
total[is.nan(total)] <- NA
count <- rowSums(!is.na(item.f))

#but now, we need to do the next step one at a time (I think)
for (subj in 1:n.obs) {
if (count[subj]> 0)  { #just do cases where we actually have data
newscore <-  NULL
score <- item.f[subj,] #just the items to be scored
for (i in 1:ncol(item.f)) {  #Treat the items as a series of 1 or 0 responses  - but note that cat = max - min
if(is.na(score[i])) {newscore <- c(newscore,rep(NA,cat)) } else {
if(very.close(score[i],( cat))) {newscore <- c(newscore,rep(1,cat))
} else {
newscore <- c(newscore,rep(1,score[i]),rep(0,cat-score[i])) }

}}
beta=discrim.F.vect[!is.na(score)]  #does this handle  missing values  -- need to fix?
delta=diffi.vect[!is.na(score)]

if((very.close(total[subj],min.item)) | (very.close(total [subj],(max.item+min.item)) )){ # first check for all lowest responses or all highest responses
if(very.close(total[subj],min.item)) { # The case of all wrong

#we need to make sure that this value is less than any value for non=minimal responses
#do the same thing that we do for the score.irt.2

if(mod =="logistic") {
myfit <- optimize(irtLimit.2par,bounds,beta=discrim.F.vect,delta=diffi.vect,scores=newscore)} else {myfit <- suppressWarnings(optimize(irtLimit.2par.norm,bounds,beta=discrim.F.vect,delta=diffi.vect,scores=newscore)) }

theta[subj]  <- myfit\$minimum
fit[subj] <- myfit\$objective

} else {
if(very.close(total [subj],(max.item+min.item))) {#all right
if(mod=="logistic") { myfit <- optimize(irtLimit.2par,bounds,beta=discrim.F.vect,delta=diffi.vect,scores=newscore) } else {
myfit <- suppressWarnings(optimize(irtLimit.2par.norm,bounds,beta=discrim.F.vect,delta=diffi.vect,scores=newscore)) }
theta[subj] <- myfit\$minimum
fit[subj] <- myfit\$objective

}}

} else {  #just process those items where we have some responses  that are neither max nor min
if(mod=="logistic") { myfit <- optimize(irtLimit.2par,bounds,beta=discrim.F.vect,delta=diffi.vect,scores=newscore) } else {myfit <- suppressWarnings(optimize(irtLimit.2par.norm,bounds,beta=discrim.F.vect,delta=diffi.vect,scores=newscore)) }
theta[subj] <- myfit\$minimum
fit[subj] <- myfit\$objective  #fit of optimizing program
}

} else {
fit[subj] <- NA
theta[subj] <- NA
}    #end if else
}

if((!is.null(keys)) & (all(keys[,f] == -1) )) {theta <- -theta
total <- -total}
theta[theta < bounds[1]] <- bounds[1]
theta[theta > bounds[2]] <- bounds[2]

scores <- list(theta,total, fit)
return(scores)

} #end of big function

##the start of the irt.poly.function after setting up the various subfunctions
min.item <- min(items,na.rm=TRUE)  #uses local minima --probably  problematic for small number of items
items <- items - min.item #this converts scores to positive values from 0  up
max.item <- max(items,na.rm=TRUE)  #we use this when reverse score -- but note that this is not the original max value.  We will adjust this in total
nf <- length(stats\$difficulty)
n.obs <- dim(items)[1]
nvar <- dim(items)[2]

#mcmapply for parallel, mapply for debugging
scores   <-  mcmapply(big.poly,1:nf,MoreArgs=list(n.obs=n.obs,stats=stats,items=items,keys=keys,cut=cut,bounds=bounds,mod=mod))

scores <- matrix(unlist(scores),ncol=nf*3)
scores <- scores[,c(seq(1,nf*3,3),seq(2,nf*3+1,3),seq(3,nf*3 +2,3))]
colnames(scores) <- paste(rep(c("theta","total","fit"),each=nf),1:nf,sep="")

return(scores)
} #end of score.irt.poly

#################################################
#
#     The main function
#
# which in turn calls either the dichotomous scoring (score.irt.2)
# or the polytomous version (scoreIrt.poly
#operates either as score.irt (deprecated) or scoreIrt (preferred)
############################################################

"score.irt" <- function(stats=NULL,items,keys=NULL,cut=.3,bounds=c(-4,4),mod="logistic")	{
message("score.irt is deprecated and has been replaced by scoreIrt, please change your call")
scoreIrt(stats=stats,items=items,keys=keys,cut=cut,bounds=bounds,mod=mod) }

"scoreIrt" <- function(stats=NULL,items,keys=NULL,cut=.3,bounds=c(-4,4),mod="logistic")	  {
#depending upon what has already been done (in the stats object), we fire off different scoring functions
#added the tau option in switch in case we have already done irt.tau   6/29/16
#we need to adjust the discrimination order from irt.fa to match the order of the items
if(!is.null(keys) && is.list(keys)){   select <- sub("-","",unlist(keys))
items <- items[select]
keys <- make.keys(items,keys)}

if(!is.null(keys) && (is.vector(keys)))  keys <- matrix(keys)
if (length(class(stats)) > 1) {
if(!is.null(keys) && is.vector(keys)) keys <- as.matrix(keys)
switch(class(stats)[2],
irt.poly = {scores <- score.irt.poly(stats\$irt,items,keys,cut,bounds=bounds,mod=mod) },
irt.fa =   {scores <- score.irt.2(stats\$irt,items,keys,cut,bounds=bounds,mod=mod)},
fa = {tau <- irt.tau(items)  #this is the case of a factor analysis to be applied to irt
diffi <- list()

class(diffi) <- NULL
class(discrim) <- NULL
new.stats <- list(difficulty=diffi,discrimination=discrim)
scores <- score.irt.poly(new.stats,items,keys,cut,bounds=bounds)},

tau = {tau <- stats   #get the tau stats from a prior run
if(is.matrix(keys)) {nf <- dim(keys)[2]} else {nf <-1}
diffi <- list()
for (i in 1:nf) {diffi[[i]]  <- tau }
discrim <- keys
class(diffi) <- NULL
class(discrim) <- NULL
new.stats <- list(difficulty=diffi,discrimination=discrim)
if(dim(tau)[2] ==1)  {scores <- score.irt.2(stats=new.stats,items=items,keys=keys,cut=cut,bounds=bounds)} else {
scores <- score.irt.poly(stats=new.stats,items=items,keys=keys,cut=cut,bounds=bounds)}
}
)
#we should have a null case
} else {#input is probably a keys matrix but not in the case of a single item being scored
#the normal case
tau <- irt.tau(items)  #this is the case of a using a scoring matrix to be applied to irt
if(is.matrix(keys)) {nf <- dim(keys)[2]} else {nf <-1}
diffi <- list()
for (i in 1:nf) {diffi[[i]]  <- tau }
if(!is.null(keys)) {discrim <- keys} else {
# stop("I am sorry, you specified  tau  but not  keys.")  #or you are scoring a single item
diffi[[1]] <- stats\$irt\$difficulty
discrim <- matrix(1,1,1)  #as strange as this seems, this needs to be a 1 x 1 matrix
}
class(diffi) <- NULL
class(discrim) <- NULL
new.stats <- list(difficulty=diffi,discrimination=discrim)
if(dim(tau)[2] ==1)  {scores <- score.irt.2(stats=new.stats,items=items,keys=keys,cut=cut,bounds=bounds)} else {
scores <- score.irt.poly(stats=new.stats,items=items,keys=keys,cut=cut,bounds=bounds)}
}
scores <- data.frame(scores)
if(!is.null(keys)) {colnames(scores) <-c( paste(colnames(keys),"theta",sep="-"),paste(colnames(keys),"total",sep="-"),paste(colnames(keys),"fit",sep="-"))}
return(scores)
}

############ END of scoreIrt  ##################
####
#Various helper functions

very.close <- function(x,y,tolerance = .Machine\$double.eps) {
abs(x-y) < tolerance}

#####
#find tau from dichotomous or polytomous data without bothering to find the correlations
#useful for score.irt
#modified July 14, 2016 to speed up significantly by dropping the xt <- table(x)  line

"irt.tau" <- function(x) {

x <-as.matrix(x)
nvar <- dim(x)[2]
xmin <- min(x,na.rm=TRUE)
xmax <- max(x,na.rm=TRUE)
nvalues <- xmax-xmin +1
if(nvalues > 10) stop("You have more than 10 categories for your items, polychoric is probably not needed")
#xt <- table(x)   #this can take a long time for sapa data

#nvalues <- length(xt)  #find the number of response alternatives
if(nvalues ==2) {tau <- -qnorm(colMeans(x,na.rm=TRUE))
tau <- as.matrix(tau)
rownames(tau) <- colnames(x)}  else {
if(nvalues > 10) stop("You have more than 10 categories for your items, polychoric is probably not needed")
#xmin <- min(x,na.rm=TRUE)
xfreq <- apply(x- xmin+ 1,2,tabulate,nbins=nvalues)
n.obs <- colSums(xfreq)
xfreq <- t(t(xfreq)/n.obs)
tau <- qnorm(apply(xfreq,2,cumsum))[1:(nvalues-1),]  #these are the normal values of the cuts

if(!is.matrix(tau)) tau <- matrix(tau,ncol=nvar)
rownames(tau) <- paste0(xmin:(xmax-1))
colnames(tau) <- colnames(x)
if(dim(tau)[1] < dim(tau)[2]) tau <- t(tau) #rows are variables, columns are subjects
}
class(tau) <- c("psych","tau")  #added the tau class so score.irt can use the tau values
return(tau)
}

"irt.responses" <-
function(theta,items, breaks = 11,show.missing=FALSE,show.legend=TRUE,legend.location="topleft",colors=NULL,...) {
#if(is.null(colors)) colors =c("gray0", "blue3", "red3", "darkgreen", "gold2", "gray50", "cornflowerblue", "mediumorchid2")
if(is.null(colors)) colors =c("black", "blue", "red", "darkgreen", "gold2", "gray50", "cornflowerblue", "mediumorchid2")
#legend.location <- c("bottomright", "bottom", "bottomleft", "left", "topleft", "top", "topright", "right",  "center","none")
#uniqueitems <- unique(as.vector(unlist(items)))
item.counts <- names(table(as.vector(unlist(items))))
uniqueitems <- as.numeric(item.counts)
nalt <- length(uniqueitems) + 1 #include the missing value from response.frequencies
nvar <- ncol(items)
theta.min <- min(theta,na.rm=TRUE)
theta.max <- max(theta,na.rm=TRUE)
binrange <- cut(theta, breaks = breaks)
binnums <- as.numeric(binrange)
items <- as.matrix(items)
stats <- by(items,binnums,function(x) response.frequencies(x,uniqueitems=uniqueitems))
stats.m <- unlist(stats)
stats.m <- matrix(stats.m,ncol=nvar*nalt,byrow=TRUE)
theta <- seq(theta.min,theta.max,length.out=breaks)
for (i in 1:nvar) {
plot(theta,stats.m[,i],ylim=c(0,1),typ="l",xlab="theta",ylab="P(response)",main=paste(colnames(items)[i]),col=colors[1],...)
for(j in 1:(nalt-2+show.missing)) {
points(theta,stats.m[,i+nvar*j],typ="l",lty=(j+1),col=colors[j+1 ],...)
}
if(show.legend) { legend(legend.location, paste(item.counts[1:(nalt-1 + show.missing)]), text.col = colors[1:(nalt-1+show.missing)], lty = 1:(nalt-1+show.missing), ncol=4,bty="n")}
}}

#developed based on suggestions and code by David Condon
#scores multiple scales with full 2pl parameters
#gets around the problem of tau differences for 0/1 and 1/6 scales.
#Requires finding the correlation matrix for each scale, rather than taking advantage of a prior correlation matrix
#modifed Jan 3, 2017 to reverse key scales where the keys and the factor solution are backwards (e.g., stability vs. neuroticism)
#modified August, 2017 to handle the case of single item scales

scoreIrt.2pl <- function(itemLists,items,correct=.5,messages=FALSE,cut=.3,bounds=c(-4,4),mod="logistic") {
nvar <- length(itemLists)

select <- sub("-","",unlist(itemLists)) #select just the items that will be scored
select <- select[!duplicated(select)]
items <- items[,select]  #this should reduce memory load
#we turn off the sorting option in irt.fa so that the item discriminations match the scoring order
#small function is called using parallel processing
smallFunction <- function(i,selection,correct,cut=cut,bounds=bounds,mod=mod) {
direction <- rep(1,length(selection[[i]]))
neg <- grep("-", selection[[i]])
direction[neg] <- -1
select <- sub("-","",selection[[i]])
selectedItems <- as.matrix(items[,select,drop=FALSE])
if(NCOL(selectedItems) > 1 ) { #The normal case is to have at least 2 items in a scale
if(!messages) {suppressMessages(stats <- irt.fa(selectedItems,correct=correct,plot=FALSE,sort=FALSE))} else {
stats <- irt.fa(selectedItems,correct=correct,plot=FALSE,sort=FALSE)}
flip <- sum(sign(stats\$irt\$discrimination * direction))
if(flip < 0 )  stats\$irt\$discrimination <-  -stats\$irt\$discrimination
scores <- scoreIrt(stats,selectedItems,cut=cut,bounds=bounds,mod=mod)
} else {stats <- list()   #the case of a single item to score
stats\$irt\$difficulty <- irt.tau(selectedItems)
stats\$irt\$discrimination <-  1
scores <- scoreIrt(stats,selectedItems,keys=NULL,cut=cut,bounds=bounds,mod=mod)
}

scores <- scores\$theta
}
#use mapply for debugging, mcmapply for parallel processing
#items is global and not passed to save memory
scoresList <- mcmapply(smallFunction,c(1:nvar),MoreArgs=list(selection=itemLists,correct=correct,cut=cut,bounds=bounds,mod=mod))
colnames(scoresList) <- names(itemLists)
return(scoresList)
}

#A perhaps more robust way of calling scoreIrt is to find tau just for a few items at a time and then scoring one scale at a time.
#the alternative is use scoreIrt for all of them at once with a keys function.

scoreIrt.1pl <- function(keys.list,items,correct=.5,messages=FALSE,cut=.3,bounds=c(-4,4),mod="logistic") {
select <- sub("-","",unlist(keys.list))
select <- select[!duplicated(select)]
items <- items[,select]
nf <- length(keys.list)
fix <-  is.numeric(keys.list[[1]])   #what does this do?

smallFunction <- function(i,keys.list,correct,cut=cut,bounds=bounds,mod=mod) {
list.i <- keys.list[[i]]
keys <- rep(1,length(list.i))
neg <- grep("-", list.i)
keys[neg] <- -1
select <- sub("-", "", list.i)
# select <- colnames(items)[select]
selectedItems <- as.matrix(items[,select])  #if items is a matrix, we need to specify all rows
stats <- irt.tau(selectedItems)
scores <- scoreIrt(stats,selectedItems,keys,cut=cut,bounds=bounds,mod=mod)
# stats <- irt.tau(items[select])
# scores <- scoreIrt(stats,items[select],keys,cut=cut,bounds=bounds,mod=mod)

scores <- scores[,1]
}
#use mapply for debugging, mcmapply for parallel processing
#items are global and not passed
scoresList <- mcmapply(smallFunction,c(1:nf),MoreArgs=list(keys.list=keys.list,correct=correct,cut=cut,bounds=bounds,mod=mod))

colnames(scoresList) <- names(keys.list)
return(scoresList)
}

#################################
#The following are useful demonstration functions for examining how fitting works
#
# Might make public if we document them
#
#############################################

#show how the fitting function works for the case without limits on the fits
#demonstrates the problem of all wrong or all right
#Also shows the difference between normal and logistic fits
###############
testIrt <- function(score,delta,beta,mod="logistic",limits=TRUE,lower=-4) {x <- seq(lower,-lower,.1)
y <- x
if(limits) {
for(j in 1:nrow(score)) {scores <- score[j,]
for (i in 1:length(x)) {if(mod=="logistic") {y[i] <- irtLimit.2par(x[i],delta,beta,scores) } else {y[i] <- irtLimit.2par.norm(x[i],delta,beta,scores)}
}
plot(y ~ x)
for(k in 1:length(scores)) {
text( -1 + .5*k,(max(y) + min(y) )*1/3,(scores[k]))}
text(0,(max(y) + min(y))/2,round(x[which(y == min(y))],2))
}} else {
for(j in 1:nrow(score)) {scores <- score[j,]
for (i in 1:length(x)) {if(mod=="logistic") {y[i] <- irt.2par(x[i],delta,beta,scores) } else {y[i] <- irt.2par.norm(x[i],delta,beta,scores)}  }

plot(y ~ x)
for(k in 1:length(scores)) {
text( -1 + .5*k,(max(y) + min(y) )*2/3,(scores[k]))}
text(0,(max(y) + min(y))/2,round(x[which(y == min(y))],2))
}
}
}

#an alternative, and much simpler model (but that does not handle missing data)
simpleScore  <- function(scores,delta,beta,mod="logistic") {
if (mod=="logistic") {estimate <- (-(scores %*%log(1/(1 + exp(-beta*delta))) - (1-scores)%*%log(1-1/(1+exp(-delta*beta)))))
plog <- rowMeans(estimate)
} else {
estimate <- -1*(((scores)%*%log(beta*(1-pnorm((delta)))) - (1-(scores))%*%log(beta *pnorm(delta))))
plog <- (rowMeans(estimate))}
return(plog)
}

#removed links to ltm since ltm does not work for polytomous data
test.irt <- function(nvar = 9, n.obs=1000,mod="logistic",type="tetra", low=-3, high=3,seed=NULL) {
if(!is.null(seed)) set.seed(seed)
if(type =="tetra" ) { x.sim <- sim.irt(nvar=nvar,n=n.obs,low=low,high=high,mod=mod)} else { x.sim <- sim.poly(nvar=nvar,n=n.obs,low=low,high=high,mod=mod)}
x.irt <- irt.fa(x.sim\$items[,1:nvar],sort=FALSE,plot=FALSE)
#if(!requireNamespace("ltm")) {stop("The ltm package is required when running  test.irt")}
# x.ltm <- ltm::ltm(x.sim\$items~z1)
#	x.ltm.sc <- ltm::factor.scores(x.ltm)
#	ltm.responses <- table2df(x.ltm.sc\$score.dat,x.ltm.sc\$score.dat[,nvar+1])
#	ltm.responses <- data.frame(ltm.responses[,c(1:nvar,nvar+3)])
#	colnames(ltm.responses) <- c(colnames(x.sim\$items),"ltm")
#	ltm.responses  <- dfOrder(ltm.responses,c(1:nvar))

xnvart <- data.frame(x.sim\$items,theta = x.sim\$theta)
xnvart <- dfOrder(xnvart,c(1:nvar))

x.fsall <- psych::factor.scores(xnvart[1:nvar],x.irt\$fa,method="regression")\$scores
x.df <- data.frame(xnvart, fs=x.fsall)
#cor2(x.df,ltm.responses)

xdelta <- x.irt\$irt\$difficulty[[1]]
xbeta <- x.irt\$irt\$discrimination
x.scores <- data.matrix(x.df[1:nvar])
irt.sc <- scoreIrt(x.irt,x.scores)
irt.scn <- scoreIrt(x.irt,x.scores,mod="normal")
ras <- 1
x.tot <- rowSums(x.scores[,1:nvar])

if(type=="tetra") {
pl2<- simpleScore(x.scores,xdelta,xbeta)
pl1<- simpleScore(x.scores,xdelta,rep(ras,nvar))
pn2 <- simpleScore(x.scores,xdelta,xbeta,mod="normal")
pn1<- simpleScore(x.scores,xdelta,rep(ras,nvar),mod="normal")

x.df.sc <- data.frame(logist2pl=pl2,pl1,pn2, pn1 ,x.tot, fs =x.df\$MR1,irt.sc[,1],irt.scn[,1],theta=x.df\$theta)
colnames(x.df.sc) <- c("PL2", "PL1", "PN2", "PN1","total", "factor","irt","irt-N","theta")
} else {x.df.sc <- data.frame(x.tot, fs =x.df\$MR1,irt.sc[,1],irt.scn[,1],theta=x.df\$theta)
colnames(x.df.sc) <- c("total", "factor","irt","irt-N","theta")}

pairs.panels(x.df.sc)
invisible(x.df.sc)
}
```

## Try the psych package in your browser

Any scripts or data that you put into this service are public.

psych documentation built on Oct. 31, 2018, 5:04 p.m.